Sometimes people say that water is removed from clothes in a spin dryer by cem;sady), kx fi+:itf-ntrifugal force throwing the water outward. What is wrong with th;f+s):y,fim it-xkd ais statement?

Will the acceleration of a car be the+lc5pxzn m ycwt htp44/bhw8a,;/:py same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spe4tl/c8mbp; w:nca4 zh /hy5+p ,ptyw xed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exogwg0:p eo2pqh492ti shc2 4vert the greatest and least forces on the road: (a) at the top of a hill, (bpqh2v2gh9 i0s4:wp ogct4e o2 ) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-gorfk. r(ta.3sj9h dmg 8-round. Which jt.kfh 3(8 9rmargs. dof these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vg( rn6o*wy*v) e(jd uggnu- a;ertical circle without the water spilling out, even at the top of the circle when the bucket(nny( evwgdg ug*oj ;*ru-6)a is upside down. Explain.

How many “accelerators” do you /h97z2 pe kyps lt-rj:have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? Wh7jt/-:sler9 h y2pkpzat accelerations do they produce?

A child on a sled comes flying over the crest of a small hill1ufpw7nwk 94 lyw8 c4q, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force beulw 8 1k f9yq47wwp4nctween his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curbyd:xx8d)-ge2 q4+ wo goo6crve at high speed?

Why do airplanes bank when they turn? Hol tj.:iolx(x4w would you compute the banking angle given its speed and radius x.j(l:lx t i4oof the turn?

A girl is whirling a i*p2g4 vqyj c62hpwx, ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she ,yq g 64hpx2 wji2pv*clet go of the string?

Does an apple exert a gravitational force on the Earth? Ifsj9vwppi nb8; 33u+ qi so, how large a force?93pb qs;v3juii+ p wn8 Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the m61 iw bso2+g. iqdzaqat421cMoon’s orbit be diff4 s1t22m ioq 1azqgdi+w6cb.aerent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on tjytla9dbqx:r84n l p7z2g4 2khe Earth? Which accelera:z4 2yx4d7lpr8gtn9 2lbqakjtes more?

The Sun's gravitationale5t kk,n z9sdfa:)p.r pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference i 9kdf )sne z.r:tk,5apn gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at.nb;0y4 hsw(6g n iymg the poles? What two effects are at work? Do the bw n.(i;4n6ymgsg0 yhy oppose each other?

The gravitational force on thedqtfj g3m61o7c )bj q) Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled )j)g6j od3m 1qqftcb7away from the Earth?

Is the centripetal acceleration of Maoa 4fz9lf36og rs in its orbit around the Sun larger or smaller than t6zaff4 ol9go 3he centripetal acceleration of the Earth?

Would it require less speed to launch a satelqni, l y fc0 xl44mjy3+bvj/:zlite (a) toward the east or (b) toward the west? Consider the E440lbxf:m jvqzy c3+ nyli ,/jarth’s rotation direction.

When will your apparent weight be the grep.4kxeh :o : 5asmf yq3x9l:qdatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upwa 9sxf4 5ld.y q:pxm3ahqe::ok rd, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space couldb0sgqv9u7a5) xn-d 7 sw. ynpz be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the 5z asb pusgn -y0)9.7wx7 vqndforce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experience9p((r4o/.rsu4iul 20npzl l p2ufe q1q1 dtaxs “free fall” or “apparent weightlessness” between (pl0roir/n .2pp(l4sa9fzue 1l 12qt4uuq dxsteps.

The Earth moves faster in its orbit around the Sun in Janu y242p/p6 nng3,je) q vq)wcczkh pau6ary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producinpaj)qnw)e/c4,y3k6u qg6vhp zncp 22g the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knov ci n2mvc*z: ):ngdf( ypn9/own until it was discovered to have a moon. Explain how this discovery enabled an estimate of Plutg) do*/9 :( 2cpvz infcnny:mvo’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moj2e8anulx:m (-h qe+lon's. Yet the Moon's is ln:8-mx(j 2 haeeqlu+mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19k ko+ )wgwoey1/ 6e/jje0ibt 680 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Efj)xpca676u7nis* zz8 . gozxarth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radi6fz)nsx 8 p*. uo77zac6ixjgzus 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2;xj zkfd ilv ,gyia1.hl+mb5 6f vd1*5.0-kg discus as it rotates uniformly in a horizontal czdf +,1jl6ix.1 vaygkhlfm di55* b;vircle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the45*1q:lb q)d.luycrnupca r6 Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational accelerat4lu6d1 *)racp c u5y.rqb nql:ion at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speckas a q(i9jzl5(5iz z8lo3ypr0 of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minut ajrlaoq3z8z p((s il0595 izye) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i2 wuc7jgtp/3p71e6u e2iy uzcn a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itip7cpj73uuz1t2/ec y62 ewg us speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a t3ja a1g,wd ,3,q*zrhti gbvf,urn of radius 77 m on a flat road if the coeffi, aq3 gv d,3*ait1bhjzfr,,wg cient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static cy8c3;4czf wcea *bubq83a;gn*n , bq friction be between the tires and the road if a car is to round a level curve of radius 85 m at a scc*3cq4a w ,8*ec;8bnzyg3 qa bfbun;peed of 95km/h ?   

  A device for training a(zclw*k4rs( e( p0k yzstronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radiussrzc4k((pkz0w el* (y 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable 7n6a:odkmu* qp ec sqtm1975h speed. When the speed of the turntable is slowl ut*9 1e m n:sm6a57qhc7kqdopy increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mus-ym4d2ohy r sfs00r uyit:+f 0t a roller coaster be traveling when upside down at the top ofoy0:s fs0y0 i4mrh t2yfurd+- a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top 7kuo8d ckn-* dwya. :dof a hill (radius =9un.a8ykco d-d* k:7wd5$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need tox1vc f qxn8)o-)e)xfduz5un 4 make for the passengers to feel “weightless” at the topmost point? zx8fe)5on-x nqx)v 4)cu f1du    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circ) k)fxh) flhv:u/ o*3b0oxfs sle of radius 1.10 m. At the lowest point of 03ff u/s*xh ))vk hobfoslx:)its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rhze.ctml*hv 3// vy,sj9pa2y/d*k /3tl x bgtotate if a particle 9.00 cm from the axis of rotation is to experience. yv*l*lyzhk 3v/txtgmdscb2 j/ /9p,h /3ate an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylinu 55:h h 53qwmap-sczbdrically walled "room." (See Fig. -c3hps5:zhq5w mub5a 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circego4dmf(r1,hb7; xa s+ )fzfb e(lw-b le on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throughg-,f(r w1ba fb+lz4se ; (xodbmfe)7h a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this f 5ehh3u2ti)p*roy8 q time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitud*u5hef28p h)3oity qre of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 mlpoj 9b5z4aguqp86 - k is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses trnn.s-e(qu n5;ileh2:x5jq $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasivet5 u) t. w,wp9jneyvk( maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted odk 29w:sys 5keie4uon* 1cr6 bn the car (by the ground) in y41k6 *ner bi2d ous5kc e9:swExample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolttkjo6,m.y)u z w0zl,yc )3j lis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this accele).lckm3u ytl),6jtzoy 0 j,zwration with no slipping or skidding? $\approx$   

  A particle revolves l-9b0i 2ew n3 2tznzwtin a horizontal circle of radius 2.90 m . At a particular instanb2t9znel2ziwwn3 0 t-t, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of :.qirebdnh647zg p* nEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earp zre 6 d:bg.h*q47ninth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the lcaq( 5irj *h lc-p;2vgravitational acceleration g has a magnitujc(;5 -il*2 plrc haqvde of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's ra1 ,0 p7pdqjv/ebzl cqcm6b ))kdius is 1.74 jpl6/,)kq pd ) 1q70mevbczbc$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timej fx*92hclbi f92r )ets that of Earth, but has the same mass. What is the acceleration due to gravity nec*fjh2i e9lf)b9 r tx2ar its surface?   

  A hypothetical planet has a mass 1.66 times th5hg d99jndm m3at of Earth, but the same radius. What is g near its surfacm9g3m 9n5 ddjhe?   

  Two objects attract ea lx og:cj8w3p(ch other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gr jv7ubixty ;;s4e*ra-avity, at (a) 3200 m 4byvu -j ;s*extia ;7r   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point o,gns1+.ta))s p s3lc fkb pf1nutside the Earth where thegravitation3ps) sgf sa+ln,n) f.tpc1 k1bal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pz 0uwvt+5 d)oy+c8kda /ojyz)acked into a sphere about 10 km in radius. Estimate the surf udo)z5c+ dy)8kwjotz y+v0/a ace gravity on this monster.    $\times10^12$

  A typical white-dwarf star, h rpck 9 s1cd5; utv9cy/n/p,v laz;,swhich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of z vcvdc;p ta 5yk1 n/psc/rs9,;uh,9lour Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astcjmb-9firo: 9 wy h,9yronauts feel weightless while orbiting in the space shuttle. Your friends respond that thwyr9ycfi9-ojh9 m:b, ey thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side ou*pt sscd(b;ew.:c.s7 rjr*tu m.z00.60 m. Calculate the magnitude and directi( mrw.s*utz osus7crb ;de.*p:c.jt0 on of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of6cg mxen 84:js the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four pla8:m4n6jge x csnets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the accelerat 82sot fco 20h*adt7zj ;y1xymion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mayo2z d0 s*xaho17t;j8t yc 2fmrs.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th sq5l0;uyt ,vvw5;je,5a :-- tcbcz mwidw sl)e period of the Earth and its distance from the Sun. [Note: Compare your ae l5jwlu :5sdz-,ty mw0sit-5v; ;c,cawvqb )nswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelli4suxxk:5w .p ite moving in a stable circular orbit about the Earth at a height of 3600 kkpi4ux.:w x5 sm.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbran/-( 7dsucc.950.jkrmb6(vgef tk,kfv djit 650 km above the Earth. How fast mm.bjt -,k0( 5fjn / avkf 6d9 vducc(regk7rs.ust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical s*.cqpn+fw dt s8t57 d:cqag*epaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is .td*7atcps q *5w q:ndg+fe8c32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu- qj:cm(;+ f0sd3jaz,w3 unqqx w0ue e*pfe r+lar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does y qe+wq-0 3*+j, 0ef3xfaz(d;u qpncerm: jwsuour result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from xm/dt/;mrb9 ethe top of Mt. Everest to be plt;/x/e9 rmmdb aced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the com lt-v4yp3::w+s fesx)a /klyd g4cm6mmand module continued to orbit the Moon at an altitude of about 100 km.lk44)cpsg3dyvl+/m -e t w:asf x:6 ym How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit um 3tvei12u c( 6szml5f;, llmthe planet. The inner radsz1u vmi(; lmcfe6mlu 53, lt2ius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates onc/4,vm ncja; ecj85k+ tcnyi5ke every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rejkc/ 58c+imc ,neva5tyj; n4k al weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astl e)7e)1 -n,e3lpu/(omf xtcz 4ulovxronaut 4200 km from the center of the Earth's Moon in a spam7ue,/zueex(3flx )4n pvo ll t co)-1ce vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mma(a1n5 1gej2 d):qybzm n;ztass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point (n2t qe1z1:ybm)admn zjg5 ;amidway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fomd,wxbe9c i 1kaku;:6r the weight of a 55-kg woman in an elevator that movewdi96u;a mk,x1 bk:c es
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from t3 9bel pr1 d.btre*aj0r+pv ,bfzg-i,he ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dibdb + j3e.gz0-ppaf*lerv,i1bt rr9 ,rection)? a =   

Show that if a satellite orbits very ne1 px7df- ppjm rn:k0r)ar the surface of a planet with period T , the density (mass mp70)nd-1jxp :pfrrk/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period ofyx5+ ey0 .)eal v27a, kcevxsu an artificial slvv+eaae,5yse 7)x2y.u k 0cxatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters-tyl kz8vyhtll5j-x -p250fx across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sut j-l 5vfxlk5-yt 0x8-2zlphy n?    $\times 10^{11}$

  Neptune is an average distance of 4.5 o1k q erh )mhhj;0,8)zitfxk7 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very closemo6ate)g :: wn6ut*z u to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from theu6 ntgu mo:):t za*w6e Sun.]    $\times 10^6$

  Our Sun rotates about the center obnomuy2bm *r; 1jj/y)f the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mbl+8zr,ar pa4oons of Jupiter (those discoveredza+,8 apb lrr4 by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth f d0 lz3+tvuqx2rom the known period and distance of the Moon. x+30u2ltvdq z   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiny.d)5+ra ymf11je z j nl0i*nxj/8m o3hvt3g ug Kepler’s third law. Use the distance of Io and the peri3im*1 xfy/je a0n tn35o)g1rhm udjj8.+vylzods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consistsht:,o2m.o,4dpp ns au of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed). t,o .op2:hd punma,s4
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form y q1ymc3r y9c*x iz4 bcjn48)rof a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance tozc1)xycj 4b*im r 94cny38y qr the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge oh w ol;t5s;n7by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate ;5ot;7ohs l nwat the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accec r*wr.p9wy md7*96 skglik 6v l/xm*sleration of gravity be half what it is on the.sv i7scp*y wxk dl m6m*/r6k r9glw*9 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mu:ea 6qd8e+ 2v8h txvxgok6y r2tual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are x8dg2a ert 6 v k2oy8:ehvqx+660.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, thc p./- fi+epc u//ixdge apparent acceleration of gravity at the equator is slightl/ di/-cugi+.xcf /pepy less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fromug1t;c74t q:gdd3 vvb the Earth to the Moon experience zero net force because the q dtgv dvt4cg:; 17ub3Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elc0ei(cm3ze068dw ny wmj(4fxevator, it says your mass is 82 kg. What is the acceleration oc if zcmjwy((6x0de034 n 8mwef the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stbl+ b37 z,xc9x hg.vtkation consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube h+h3,txk.v9l bc x gz7bas a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43s.( gt) ;rgpst).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for th25bjmzuk 6xe:v bbvep-*-rg .p/kz,u e mass of a planet in terms of its radius r, the acceleration vg/-ke*bmku-xb,p ez2 vu5 z.:pbj6rdue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m h --hynrgftje7e +y0y 59a0dyf 1llob/anging on a string) is deflected from the vertical by an ae/00ly5 ydy1 9yej-7fh + fgantlr-o bngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design8 ;otby1,esq t speed of If the coefficient of static friction is 0.30 (wet pavement) oy,1 eb;ttqs8, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were 5w:bjw 5ibieqk +muj58zc-;n rotating so fast that objects at the equator were apparently weightless? :nwcj855w5 q z+;mbb-uk eji i   $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o )u 8(dljshf csy+yj-jon5(, l7t gnp2f 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of bs .4 lzfr /mkv +h(rkdp(fp*-radius 235 m. A lamp suspended from the ceiling swings out .4-fplh*pr sbfk/k vr ((z dm+to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 tny41;y-n5bm4 :wx8aa 9rc l9p tcnjft; obc)n imes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number axc;m9r9njbtwn4a; l8yn)bcyt p15:n o- fc4of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of annlcaf 72se* (lfl+hz- extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapen ll+*2l(f f-hs 7acezs). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown idg h9* ;nj2dwrn Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would therj2h;dg nwd9* driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning 9 n ak zl;hs)4(acq-fxSystem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and ahfc)9zl ;x n-4kas (qsignals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmfyte5q; u,c; p, is meant to orbit the asteroid E;y p,ectu;q 5fros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a uytyxj,-et5tu,mpw .r 6w 44msatellite in need of repair. You are in-m4.5 xtrjptu ,w6euy ywm,4t a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp o3cu:lywspa. 3qt-9: prf au8has a period of 3000 years. (a) What is its mean distance from the Su u.w9lf-: typ:qas3 rpauo3c8n?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would nu v8 q)fp:igi(lvjx)/eed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable a)uix g)q:pli(vf/ vj8ssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gaebe(6:m q ia3wxwkp.f. ) p4uclaxy (Fig. 5-46) at a distance of about 30,000 light-years fr :m6)cf.4buai wepk( wxe.p 3qom the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a se m;tohwh0 m2u ycq-).quare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the wt q0 -m ch.)u2mh;oeysquare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kgqei,k5z;w7d: 3jk;*nup mjs v d6 rw1j orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweepy:s zq9v a7ma m ,*ec3kpqcn*3 second 3, ymcq* e9zqn3sa 7mvak :pc*hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to 0sy eq btifh-09 q5mh 8ewpvac, 64z(yswing a sinker weight around in a circle below you on a 0.25-m piece of fishing,hezc h5qv0-96( q0amfwt iy4 ey8sb p line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is d3 ti2n 02wpzb3pglnt 3esigned so that a car traveling at spe33z2gt ltipp3nn b w02ed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whegw2; -j kl-jyu-ofnc +n negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration,-c;f - wj-o nlku2+jgy is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$